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# Discovering Right angles: Proving Perpendicular Diagonals in a Square

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Question: A square PQRS has vertices P(2, 4) , Q(6, 8) , R(10, 4) and S(6, 0) . Which set of steps should a student follow to prove that the diagonals of the square are perpendicular to each other? Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1=−m2 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1+m2=−1 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1=m2 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1×m2=−1 .

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The correct set of steps a student should follow is: Step 1: Find the slope of diagonal PR (m1) and slope of diagonal QS (m2). Step 2: Show that m1×m2=−1. This is because in geometry, two lines are perpendicular if the product of their slopes is -1. If m1 and m2 are the slopes of the two lines, then m1 * m2 should equal -1 for the lines to be perpendicular. Hence, this is the correct set of steps to prove that the diagonals of the square are perpendicular to each other.

Jan. 12, 2024, 8:30 a.m.

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